- Tytuł:
- Backbone colorings along stars and matchings in split graphs: their span is close to the chromatic number
- Autorzy:
-
Broersma, Hajo
Marchal, Bert
Paulusma, Daniel
Salman, A. - Powiązania:
- https://bibliotekanauki.pl/articles/743123.pdf
- Data publikacji:
- 2009
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
backbone coloring
split graph
matching
star - Opis:
- We continue the study on backbone colorings, a variation on classical vertex colorings that was introduced at WG2003. Given a graph G = (V,E) and a spanning subgraph H of G (the backbone of G), a λ-backbone coloring for G and H is a proper vertex coloring V→ {1,2,...} of G in which the colors assigned to adjacent vertices in H differ by at least λ. The algorithmic and combinatorial properties of backbone colorings have been studied for various types of backbones in a number of papers. The main outcome of earlier studies is that the minimum number l of colors, for which such colorings V→ {1,2,...,l} exist, in the worst case is a factor times the chromatic number (for path, tree, matching and star backbones). We show here that for split graphs and matching or star backbones, l is at most a small additive constant (depending on λ) higher than the chromatic number. Our proofs combine algorithmic and combinatorial arguments. We also indicate other graph classes for which our results imply better upper bounds on l than the previously known bounds.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2009, 29, 1; 143-162
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł